The E_2-term of the descent spectral sequence for continuous G-spectra
Algebraic Topology
2007-05-23 v2
Abstract
Let {X_i} be a tower of discrete G-spectra, each of which is fibrant as a spectrum, so that X=holim_i X_i is a continuous G-spectrum, with homotopy fixed point spectrum X^{hG}. The E_2-term of the descent spectral sequence for \pi_*(X^{hG}) cannot always be expressed as continuous cohomology. However, we show that the E_2-term is always built out of a certain complex of spectra, that, in the context of abelian groups, is used to compute the continuous cochain cohomology of G with coefficients in lim_i M_i, where {M_i} is a tower of discrete G-modules.
Keywords
Cite
@article{arxiv.math/0602480,
title = {The E_2-term of the descent spectral sequence for continuous G-spectra},
author = {Daniel G. Davis},
journal= {arXiv preprint arXiv:math/0602480},
year = {2007}
}
Comments
8 pages. Main result simplified. Expository Section 3 added. Error in Definition 2.1 is repaired. Same as published version, except for changes required by journal's style file